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Exercise

Numerical tests of normality

The moments package contains functions for computing the kurtosis and skewness of data and well as for implementing the Jarque-Bera test, which is a test of normality based on these higher-order moments. In one command, it compares the skewness and kurtosis of the data with the theoretical values for the normal distribution, which are 0 and 3, respectively.

jarque.test(x)
skewness(x, na.rm = FALSE)
kurtosis(x, na.rm = FALSE)

In this exercise, you will calculate the skewness and kurtosis for the djx, the Dow Jones index from 2008-2011, and apply the Jarque-Bera test of normality. You will then apply the same methods to djreturns, which contains 29 of the Dow Jones stocks for the same period.

Recall that you can use apply(X, MARGIN, FUN, …) to apply functions over array margins. The MARGIN parameter is a vector indicating where the function will be applied; in this instance, you will use 2 to specify that the function FUN should be applied to the columns in matrix X.

The moments package has been imported for you, and the djx and djreturns data is in your workspace.

Instructions

100 XP
  • Calculate the skewness and kurtosis of the Dow Jones index returns in djx using skewness() and kurtosis(), respectively.
  • Carry out a Jarque-Bera test of normality for djx using jarque.test().
  • Use apply() to calculate the skewness and kurtosis of the individual equity returns in djreturns assigning the results to s and k, respectively.
  • Fill in plot() to plot k against s with parameter type = "n", and then place the stock symbols at the points with the command text() (this has been done for you).
  • Use apply() to carry out the Jarque-Bera test for each of the Dow Jones constituents in djreturns.